Near-Optimal Echelon-Stock (R, nQ) Policies in Multistage Serial Systems

A numerical study suggests that the heuristic solutions are easy to compute (even for systems with many stages) and are close to optimal and suggests that a traditional approach for determining the order quantities can be seriously suboptimal.

Abstract

We study echelon-stock (R, nQ) policies in a multistage, serial inventory system with compound Poisson demand. We provide a simple method for determining near-optimal control parameters. This is achieved in two steps. First, we establish lower and upper bounds on the cost function by over- and under-charging a penalty cost to each upstream stage for holding inadequate stock. Second, we minimize the bounds, which are simple, separable functions of the control parameters, to obtain heuristic solutions. We also provide an algorithm that guarantees an optimal solution at the expense of additional computational effort. A numerical study suggests that the heuristic solutions are easy to compute (even for systems with many stages) and are close to optimal. It also suggests that a traditional approach for determining the order quantities can be seriously suboptimal. All the results can be easily extended to the discrete-time case with independent, identically distributed demands.